トロピカル幾何学を用いたC空間解析
C-space Analysis using Tropical Geometry
トロピカル幾何学とピュイズー級数を用いて、1自由度機構のC空間の特異点（横断的分岐やカスプ）を近似的に有理パラメータ化して検出する手法を提案した。
詳しい要約
1. どんなもの？
2. 先行研究と比べてどこがすごい？
3. 技術・手法の肝は？
4. どうやって有効だと検証した？
5. 議論はある？
6. 次に読むべき論文は？
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著者: Abhilash Nayak
分類: cs.RO
原文アブストラクト
Configuration space~(C-space) of a mechanism is a real variety describing the set of feasible configurations that it can attain. To understand the behavior of a mechanism, it is crucial to identify and scrutinize especially the singular points of its C-space. They usually appear when the variety intersects itself, leading to different branches of motion. There exist many approaches to detect those intersections if they are transversal. However, the problem remains challenging if there are tangential, cuspidal, inter-dimensional or a combination of these intersections. This paper exploits an approach acquired from tropical geometry to analyze the neighborhood of any point on C-spaces of 1-degree-of-freedom~(\emph{dof}) mechanisms. This is done by finding the approximate rational parametrization of the curve(s) passing through the given point using Puiseux series. The proposed approach is shown to succesfully detect the transversal branchings in two foldable four bar mechanisms and a cusp in the configuration curve of the double Watt mechanism.
